BeamDynamicsstudybyusingGeneticAlgorithms

andtheELI-np case

AlbertoBacci– INFN-Milano

Alberto Bacci, Laboratoire de L’Accélérateur Linéaire (Orsay – France), 13th June

q Genetic Algorithms (GAs) introductionØ Historical notesØ Hints on What are & Why use GAsØ Where: Genetic Algorithms in Beam Dynamics Optimization

q GAs applied to Beam-Lines OptimizationØ From Beam-Lines to ChromosomesØ Following Genetic Laws: Fitness, Reproduction, Mutations, …Ø E.G.: SPARC beam line Optimization in Thomson case

q The GIOTTO codeØ The Data-Based DBØ Inputs & OutputsØ Fitness function (or Idoneity) definitionØ Optimizations & Statistics on Specific Cases:

ü Ultra short bunches by Hybrid Velocity Bunchingü Comb bunches distributions

Ø Eli-np Case: The reference Working Point & Statistic

Outline

v1970 John Holland - schemata theorem

v1975 J. Holland publication: “Adaptation in Natural and Artificial Systems: AnIntroductory Analysis with Application to Biology, Control, and Artificial Intelligence”.The Seminal work

v1975 K. De Jong (J. Holland’s student), Thesis: “An analysis of the behavior of a class ofgenetic adaptive systems”. Broad applicability of GAs

v1989 David Goldberg Book: “Genetic Algorithms in Search, Optimization, and MachineLearning”

It deals with the topic at high level and is considered a milestone in GAs story. Itreports techniques like Multi Objective GA (MOGA), today very current.

q Genetic Algorithms (GAs) introduction: Historical Notes

John Holland

start

End

Local extrema

q Introduction: What & Why

What are Genetic Algorithms (GAs)Searching procedures based on natural selections (genetic laws)

Why choosing GAs versus other techniques … A basic answer:

Newton-Raphson methods (and many variants) are based on local information.The Scan moves in direction of “local maxima” or “local minima”

start

End

A Parabola

q Introduction: What & Why

Why Genetic Algorithms **

Despite, Newton-Raphson methods can overcame the local solutions issue by some

tricks …GAs are:Ø naturally able to manage the local solution issue

Ø naturally parallelizable

Ø usable with a minimum mathematical effort

And, by empiric results,show strong capability to manage problems where other methods fail

** pros and cons in literature

q Where: Genetic Algorithms (GAs) in Beam Dynamics Optimization -1

GAs give strong advantages …

Ø in multi-dimensional problems with variables strongly non linear correlated

A main example :

Ø Space Charge & its non-linear nature: correlates low energy beam-line parametersØ Also frozen beams (space charge off): Other complex situations

Example (1) Thomson/Compton Sources (e.g. SPARC_lab, STAR, ThomX, ELI-np, MunichCompact Light Source) which ask for :

For the spectral density: 1) very low DE/E, 2) low Emit

For the photon flux : 3) Qbunch as high as possible

Example (2) Ultra short e-beams (e.g. SPARC_lab, LCLS, REAGE, XFEL, EUPRAXIA, … ):

§ Femtosecond light pulses (FEL/X-FEL), Atoms in chemical reactions, phase-transition, Photosynthesis Water Splitting : timescale 1-100 fs [2014 “first snapshots of water splitting” by LCLS; ScienceDaily; Nature]

§ Plasma Wave Acceleration: λplasma order of 30-600 fs . The Witness much shorter, theDriver (pwfa) comparable to λplasma

§ Femtosecond Electron Diffraction (FED)Molecular or atomic motion movies: phase transitions, …, . Timescale: few 10s of fs.Relativistic case: Eb ≈ 5MeV, Qb ≈ 100fC, εtr<0.1 mm-mrad, σz<30μm (100fs)

§ THz radiation (by CoTrRad)0.1 up to tens THz is of great interest for both longitudinal electron beam diagnostics(fs scale) and spectroscopy in pump-and-probe experiments ....

q Where: … - 2

Genetic Algorithms applied to Beam-Line Optimization

q From Beam-Lines to Chromosomes

Genetic Laws work on Chromosomes ==> Chromosomes are made of genes (parameters)

A Beam-Line

Chromosome

=

Beam-Line = Parameters Array ==> One Chromosome

q Following Genetic Laws: Fitness Function

Chromosomes Must be sortedby a Fitness function

22

25035.0 5050÷÷ø

öççè

æ-÷

øö

çèæ-

×+×spreadEeimtX

ee==

Δγ/γεn,x +

Rules to pass generation è in generation:§ Selection: bluffed Roulette wheel§ Mutations

…. & others methods & tricks. The rule: closest to Nature, best performances

Ø Following Genetic Laws: Reproduction & Mutation

0< <100Chromosome Sorting by

sum of probability == 1

By the Roulette Wheel: two Chromosomes

Gun gradientGun Ф injection

Bz intensity first solenoid

Chromosomes reproduction

Mutation, withprobability < 1%

Trackingcode

99.97.90.85.

60.58.

Ø Following Genetic Laws: Real coding (1) and binary coding (2)

Chromosome

(2)BinaryCoding

0<GeneValue<255.127

1|1|1|1|1|1|1|1.1|1|1|1|1|1|1

0|0|0|0|0|0|0|0.0|0|0|0|0|0|0

8bits 7bits

15bitsXGeneAs DNA in Genetic Laws

Decoding to decimal and compute the fitness

(1) Genetic rules on Real Numbers Main loop,

Generation in Generation

Main loop, Generation in Generation

Genetic rules on binary arrays

Ø Following Genetic Laws: Elitism

Concluding: the elitism

Sorting

oper

+2 +5

>

Nowadays “quasi-classic” optimization techniqueso elitismo advanced mutation operators o hill climbing o regeneration from best solutionso … … …o & parallelization quasi-mandatory

Ø E.G.: SPARC beam line Optimization in Thomson case

gge D

×=

nx

fitnessF,

1

“MAXIMIZING THE BRIGHTNESS OF AB ELECTRON BEAM BY MEANS OF A GENETIC ALGORITHM”A. Bacci, C. Maroli, V. Petrillo, A. Rossi, L. Serafini - NIMB 263 (2007) 488-496

Old Kind of Fitness Function

(a) Byhand(b) ByGA

spot spectrum

The GIOTTO code

v WAS BORN in 2008; Language: Fortran 90/95

v USE for Optimization of Generic Code’s Parameters or for Statistical (Jitters) Analysis

v INPUTS based on NameList & on two internal DataBase

v CAN easily Drive different codes:Now: ASTRA’s Generator, ASTRA, QFluid (Plasma acceleration, A. Rossi modifications)

v Current Version (Ver. 10.0):Linux 64 bit; Windows 64 – (compilers gfortran or INTEL fortran)Parallelized with OPEN-MPI (Linux), MS-MPI or INTEL MPI (Windows)Used @ PSI (S. Bettoni) and tested at Desy-Pitz

v Code and Documentations: URL: http://pcfasci.fisica.unimi.it/Pagine/GIOTTO/GIOTTO.htm (server down, pardon!)Exist an User manual for version 8.5 2012 (needs updates)

GIOTTO - Genetic Interface for OpTimising Tracking with Optics

GIOTTO – GeneticInterfaceforOpTimising TrackingwithOptics

Switch from Optimizations to Statistical analysis is really EASY

Jitters sampling interval: Uniform or Gaussian

Every NameList ’s variables can be used as a GENE (optimizable) & Any code working withNameList is directly importable in GIOTTO.ASTRAe.g.:Phi(1)…Phi(50),MaxE(1:50),MaxB(1:50),sig_x (lasercathode) ,sig_clock(Laser@cathode),…,…(nolimitonthenumber)

Constraintsfreelydefinedbytheuser(undertest)

Optimizationtechniques:elitism;advancedmutationoperators; hillclimbing; antcolonyregenerationfrombestsolutions

ImportantGIOTTO’sfeatures:

From2008uptoday,thecodeisgrewinpowerand capability

user freely defined by Astra outputs:Targets: bunch PosZ or Time, En, Enspread, SigZ, Xemit, sigX, divergX, Yemit, ….

All variables usable inTHE BEAM-LINE

Now: Astra_generator, Astra, QFluid

Optimizable variables

THE GENEs

Ø GIOTTO’s Data-Bases

DB_1

Sub-DB_1

Astra Outputs (or other codes)

THE FITNESS

emittance, envelope, En_spread,etc. …

DB_2

Ø GIOTTO’s INPUT FILE

GINxx.xx.ini is divided in two parts:1) One NameList (&GA) giving all the directive to GIOTTO

2) Three keyNames defining: CONSTRAINTS, FITNESS and GENES

1)

2)

Ø GIOTTO’s INPUT FILE: &GA NameList

Under developing (it slows down heavily GIOTTO)

OptimizationRarely needs changes

Usually few variables are used

Ø GIOTTO INPUT FILE: Key_Names

Rarely needed

Comments

Comments

GENESDefinition

Definition

Ø GIOTTO: FITNESS FUNCTION

Reverse Polish Notation: Opers Follow OperandsØ 3 4 + = 7Ø Stack based operationØ Does not need brackets

Fitness Funciont strategy to Cope with Multi Objectives Problems (MO):

o One Single Criterium per Equation piece (Objectives Wights)

o To be close to the Goal mean close to the Gaussian Curve Top

o The ‘Far region’ (referring to optimization) has to be on the maximum Gaussin slope

o change the FF in real time (ander implementation)

50 # 𝑒%&'()*+.-

+

+50 # 𝑒%.(/01.2-

+

+50 # 𝑒%.(/*+.-

+

=

a) not yet full optimized

b) full optimized

GIOTTOOptimization &

Statistical analysis

2.0mdrift

Beam-Line Optimization for: ultra short, ultra cold, High brightness bunches

A Beam-Line studied with:

Ø Experience

Ø An Ad hoc GIOTTO use

GENES in the Optimization:

Ø Gun:

• (1) Phase & (2) Solenoid (Bz)

Ø TW cavity (RF- Compressor):

• (3) Phase & (4) Solenoids

Ø C-band cavity: (5) Phase

GOALS:

Ø Low Emittance

Ø Low Energy Spread

Ø femptosec. Sig_Z

C-band cavity

Drift@20MeV

ΔE=100keV

GIOTTORESULT

Emit[um]

Envelop[mm]

Sig_z[um]

GIOTTO OUTPUT: RISULTATI.TXT

GENES

RISULTATI.TXT

Generation

Id va

lue

Emit sigZ ∆𝑬

Best Chromosome of theGeneration N.5

- P.O.Shea et al., Proc. of 2001 IEEE PAC, Chicago, USA (2001) p.704.- M. Ferrario. M. Boscolo et al., Int. J. of Mod. Phys. B, 2006 (Taipei 05 Workshop)

€

10 ps← → $ $

Beam-Line STATISTIC for Laser Comb (ECHO Bunch Generations)

4Bunches

6 Bunches

360cases

Beam-Line STATISTIC for Laser Comb – TWO Bunches case : Current Statistic

GIOTTOand the ELI-NP case

ELI-NP LINAC machine

Beam Dynamic features

Electron Linac design to drive bright Compton back-scattering gamma-ray sourcesA. Bacci, D. Alesini, P. Antici, M. Bellaveglia, R. Boni et al.

J. Appl. Phys. 113, 194508 (2013); online: http://dx.doi.org/10.1063/1.4805071

The Peculiar Gamma Ray Source features

In next page,how to reach these parameters

TheEmittanceMaximizationofelectrondensityintotransversephasespace:==>means==>verylowemittance̴0.4mm-mrad

TheEnergySpreadMinimization oftheenergy spread:thesourcespectral density require Δγ/γ <0.1%,wehavechosenaconservativethresholdof0.05%

EnergySpreadbyRFcurvature:

ELI-NP Injector merit factors

σz <280µm@theinjectorexit

Boosterfreq.

Result: GIOTTO optimization on merit factors ( booster’s injector)

Comparison using Tstep (a Parmela heir) & Astra codes

1) A space charged dominated region needs a double check2) Astra gives the possibility to use Giotto (Giotto improves 30-60 %)

γε =0.4 μm<E>=79.8 MeVσz= 0.279 mmσE/<E> = 1.65%

Tstep

Astra with GIOTTOTstep

Astra

31

Injector jitters analysisa full S2E:

Injector→ C Booster → γ-SourceAstra→ Elegant → Cain

Jitters kept in Consideration in GIOTTO:

RF:Ø 200 fs Phase (overestimated): (1) Gun & (2,3) TW cavities (S- band)

Ø 2‰ in pick field: (4) Gun & (5,6)TW cavities (S- band)

laser: Ø (7) 200 fs arrival timeØ (8) 20 µm pointing instabilities (on cathode)Ø (9) 5% energy fluctuation (Charge fluctuation)

Different Machines:+/- 70 µm as misalignments for: RF Cavities, Gun Solenoid, TW Solenoid

Uniform distributions Jitters; a very conservative choice

ELI-NP booster’s Injector Jitters (9 parameters)

Alljitters

Machine_1160runs

Machine_2160runs

Machine_3160runs

34

ELI-NP Injector Jitters Analysis – Energy & Bunch length

σz

Alljitters

Machine_2160runs

Machine_3160runs

35

Machine_1160runs

ELI-NP Injector Jitters Analysis – Centroid, Envelope, Emittance

In Conclusion

Genetic Algorithms show great promise in the Beam Dynamics optimization and problemsolution.

GIOTO has been applied successfully to:• refine known beam lines, with improvements around 20-40 % (in the performances)• have been used to find completely new schemes, as in case of the hybrid velocity

bunching

Demand of EXTREME HIGHT QUALITY electron beams doesn’t stop and often it makes necessary to cope with strong space charge

Beam-Line optimization is Nowadays really a critical issue

Thanks for your attention

RF-Gun 1.6 S-band 120 MV/m

Emittanzometro’s data are handled by a dedicate algorithm thatreturn an intensity matrix PhaseSpace.txt (successively interpolatedto increase the definition)

Emittanzometro

100%97% 95%

pe area=

ea

eb

eg

e

===

=-

=++

abg

agb

axybygx

,,

112

22

22

12

2

22

=-

=++

agb

eabg xyyx

GMESA normalization

1222 <¢+¢+ xaxxbgx

1222 >¢+¢+ xaxxbgx

Emittance inRealBeam

Since real beams usually do not have well defined boundaries, a method for calculating the emittance, isto choose a specific density contour, in the phase space, that represents from the 50% (worst cases) upto the 98-99% (best cases) of the whole bunch charge (or integrated intensity). Within this densitycontour and under certain conditions, such emittance satisfies the Liouville’s theorem and thus isconserved

ea

eb

eg

===

=++

abg

axybygx

,,

1222

dfitness A

IF =

c g b a g b aOne of the 30 generation’s chromosome with 25 genes

g ab

1 2 830

The space phase ellipse’s sampling is a thornyissue as uniformity and dimension. A shuffleduniform random generator is used.

One of the more significant curve - analyzed also with two other methods - that shows a strongly markeddouble minimum

Some phase space of the emittance curve

From first tests the code seemed to be able to analyzethe rough phase space images, not yet interpolated Anoutputfile

Data analysis at SPARC - Some relevant results

Developing of a dynamic link library (dll), in fortran 90, that can interface with LabView

N. Corrector Current of maximum variation per corrector

Sample of the Correctors configurations

rms of the BPM off-set

best solution

Generation n

Generation n+1 memory of the best solution

from simulations it converges to 0.200 mm of maximum off-set after 80 generationConsidering 2s to test each configuration → 36 minutesThe real world could be faster ant colony optimization

BPMandGeneticcontrolofthesteeringcorrectorsA code to compute the rms

emittance of high brightness electron beams4